Ball — On the Binary Star f Ursae Major is. 317 
between the spring of the year 1816 and the spring of 1817. Before 
the star reached its last periastron, we have only three observations 
available ; namely, that already mentioned (1781), and two others by 
the same eminent observer in 1802 and in 1804. These last ob- 
servations, as Herschel II. remarks, having only an interval of two 
years, are of little more value than a single observation. After 1804 
there appears to have been a much to be regretted lacuna in the 
observations, the next recorded being one by Struve in 1819.^' It is, 
therefore, manifest that, during the twelve or thirteen years preced- 
ing the last periastron passage of the star, and for two years subse- 
quent to the passage, no observation has been recorded. JN'ow, in 
this interval, one star swept round the other with amazing velocity, 
accomplishing a change of position of no less than 168° in the fifteen 
years. Had a few observations, distributed over this critical period, 
been available, the additional information would have enabled these 
astronomers who have investigated the subject to have determined 
the elements of the orbit with the utmost attainable precision. So 
far as the value of observations are concerned, the most critical epoch 
is, perhaps, not that of the periastron passage, but the epoch at which 
the angular velocity of the position angle is a maximum. In the 
present case, this occurs three years previously to periastron ; thus, 
about 1814, the position angle changed at a rate exceeding 20° per 
annum, while at periastron the rate was about 13° per annum ; this 
shows still more clearly how desirable it would be to have had some 
observations between 1804 and 1819. 
iNow, however, the star is rapidly approaching its second peri- 
astron, through which it will pass early in 1876 ; consequently, the 
numerous observations of the last few years have, to a great extent, 
supplied the want of observations already referred to. It is believed, 
that by the aid of these observations, a new series of approximate 
elements have been found, which represent the entire system of ob- 
servations with tolerable fidelity. 
The angle of position of the star is now (1872), changing with 
extreme rapidity, and a careful series of observations for the next 
ten years will be of the greatest interest in sidereal dynamics. 
The elements of the four orbits already referred to, are given in 
Table I.f 
* The observations here referred to are taken from " Dawes' Catalogue of 
Micrometric Measures," M.R.A.S., vol. xxxv., p. 353. 
t Herschel, " Outlines of Astronomy," 4th Ed., p. 573. 
